Plotting True Course and Distance Between Two Charted Points

What the rule requires

The whole problem is four operations in a fixed order: identify the two points, draw the line, read the direction off the rose, measure the length off the latitude scale Bowditch Ch. 4 §406.

The straight line is legitimate because of the projection. A Mercator chart presents latitude and longitude as straight lines crossing at right angles, and a rhumb line — a track of constant bearing — plots as a straight line on it Bowditch Ch. 4 §402. One course value therefore governs the entire leg, however long, and the line you draw between the departure and the destination is that course.

Direction comes from the compass rose and from nowhere else on the chart. Walk the parallel rulers from the drawn line to the nearest rose, keeping the arms in contact through every step, and read the true course where the ruler crosses the outer ring. That outer ring is the true ring; a graduation read anywhere else is not the true course .

Distance comes from the side of the chart. Latitude is read from the left and right scales, longitude from the top and bottom, and because one minute of latitude equals one nautical mile, distance is measured on the latitude scale — never on the longitude scale Bowditch Ch. 4 §405. Which part of the latitude scale matters as much as which scale: measure at the latitude of the line, since meridian length varies with latitude . A leg lying along 24°40'N is measured against the scale abreast of 24°40'N, not against a convenient span at the top corner of the sheet.

Before the pencil touches the chart, know what the two points are. Chart No. 1 is the authoritative key to every symbol and abbreviation on the sheet, and a mariner decodes the symbols against it before plotting Bowditch Ch. 4 §404. The chart title also states the unit of the soundings, referenced to Mean Lower Low Water, which is worth confirming in the same glance Bowditch Ch. 4 §403.

The course line then gets labelled: course above, speed below . The standard form is C 090 above the line and S 8 below it, with positions labelled in 24-hour time Bowditch Ch. 8 §802. Note the leading zero. A true course is a three-digit figure, and C 090 is the form the plot carries — not 90.

Your leg runs from 24°32'N to 24°48'N. Which scale, and what part of it, gives you the distance?

The latitude scale on the left or right edge, read abreast of the leg — around 24°40'N. One minute of latitude is one nautical mile , and the measurement must be taken at the latitude of the line because meridian length varies with latitude . The top and bottom scales give longitude and measure no distance at all.

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Telling it apart

Three sets of graduations sit within reach of a plotted line, and the single criterion separating them is what each one is graduated in.

• Side scales, left and right — graduated in latitude. These give the north-south component of a position, and they are the only distance scale on the chart, one minute reading one nautical mile Bowditch Ch. 4 §405. Most often misfiled by candidates who use whichever side scale is nearest the chart border instead of the one abreast of their own leg.
• Top and bottom scales — graduated in longitude. Position only. Because they carry minutes of longitude and not minutes of latitude, a divider span carried to them yields a figure that is not a distance in miles. Misfiled by anyone whose leg happens to run east-west, because the horizontal scale looks like the natural place to lay a horizontal span.
• Outer ring of the compass rose — graduated in true direction. This is the ring the true course is read from Bowditch Ch. 4 §406. Misfiled when the ruler is read against an inner graduation and the value is then reported as a true course.

Position is stated latitude first , and a question that gives you 24°45.0'N, 081°32.5'W is naming the side scale before the bottom one for the same reason.

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Working a question

A question gives you a departure fix off the sea buoy at 24°33.0'N, 081°48.0'W at 0930, and a charted light as the destination. Four answers offer courses within a few degrees of each other and distances within a mile or two. Here is the sequence that separates them.

1. Locate and mark both points. Plot the departure by latitude off the side scale and longitude off the top or bottom scale, and identify the destination by decoding its charted symbol against Chart No. 1 Bowditch Ch. 4 §404 before you commit a pencil mark to it. Two lights half a mile apart with different characteristics are a standard trap, and the symbol is what tells them apart.
2. Join them with one straight line. On this projection that line is the rhumb line and carries a single constant course Bowditch Ch. 4 §402. Draw it fine and draw it long enough to reach cleanly toward the rose.
3. Walk the rulers to the nearest rose. Lay one arm along the line, hold it, advance the other, and repeat until an arm passes through the centre of the rose. Every step is a chance to introduce a degree of error, so use the nearest rose and take the fewest steps that will reach it.
4. Read the outer ring in the direction of travel. The ruler cuts the ring at two points, 180° apart. Your line runs northeast from the buoy, so the reading is 062, and the graduation at the other end — 242 — is the reciprocal, which is the course home rather than the course out Bowditch Ch. 4 §406.
5. Check the walk before you accept the number. Walk the rulers back from the rose to the line. If an arm no longer lies along the drawn line, the walk slipped and the course is wrong; redo it. This costs fifteen seconds and catches the error that otherwise puts you two degrees into a distractor.
6. Measure with dividers on the latitude scale at the working latitude. The leg lies near 24°40'N, so use the side scale abreast of it. Set the dividers to a round 5 minutes — 5 nautical miles — and step along the line: two full steps run 10 miles, and the remainder, carried back to the same part of the scale, spans 2.4 minutes. Distance 12.4 nautical miles Bowditch Ch. 4 §405.
7. Label the plot. C 062 above the line, S 8 below it if a speed is given, and 0930 at the departure position Bowditch Ch. 8 §802.

The answer to the question is true course 062, distance 12.4 miles. Note that steps 4 and 6 are where the answer is decided, and steps 5 and 1 are where the wrong answer is prevented.

You measured the same 12.4-mile leg by carrying the dividers to the latitude scale at the top corner of the chart, three degrees of latitude north of the leg. What have you done to your answer?

Introduced a scale error. Meridian length varies with latitude on a Mercator chart, so the graduations at the top of the sheet do not represent the same chart span as those abreast of the leg, and distance must be measured at the latitude of the line . The course is unaffected; only the distance is wrong, which is exactly what a paired-answer distractor is built to catch.

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Where candidates lose the point

Reporting the reciprocal. The rulers cut the rose twice, and the candidate reads the graduation that happens to fall on the near side of the rose rather than the one matching the direction of travel. A leg running northeast reads 062, not 242. Establish which point is the departure and which the destination before you look at the rose, and confirm that the value you read agrees with the quadrant the line runs into.

Measuring on the longitude scale. This attracts anyone whose leg runs roughly east-west, because the top and bottom scales lie parallel to the span being measured. Distance is measured on the latitude scale, never on the longitude scale Bowditch Ch. 4 §405.

Measuring on the latitude scale at the wrong latitude. Less obvious than the previous error and more common on charts covering several degrees. The requirement is to measure at the latitude of the line Bowditch Ch. 4 §402, so the divider span goes to the scale abreast of the leg.

Accepting a slipped walk. Distractors on a plotting question sit a few degrees apart precisely because parallel rulers creep. A candidate who never walks back to verify has no way of knowing which of two adjacent answers their reading supports.

Dropping the leading zero. A course of ninety degrees is written C 090 Bowditch Ch. 8 §802. On a multiple-choice sheet this rarely changes the answer chosen; on a plot it produces an ambiguous figure, and the three-digit habit is what the labelling convention exists to enforce.

Plotting to the wrong charted object. Two aids close together, one a light and one a buoy, will both sit near where the candidate expects the destination to be. The symbol and abbreviation identify which is which, decoded against Chart No. 1 Bowditch Ch. 4 §404. An error here puts both the course and the distance outside every offered answer, which is at least a signal to start again.

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Check yourself

You plot a line from a fix to a destination bearing to the southwest. Walking the rulers to the rose, you read graduations at 048 and 228. What is the true course?

1. Both graduations lie on the same ruler line, 180° apart, and the true course is the one in the direction of travel — southwest Bowditch Ch. 4 §406. Reading 048 gives the course back to the fix.

Your leg runs due east along 40°10'N on a chart whose bottom border is graduated in minutes of longitude directly beneath the line. Where do you measure the distance?

On the latitude scale at the left or right edge, abreast of 40°10'N. One minute of latitude is one nautical mile and distance is never measured on the longitude scale Bowditch Ch. 4 §405, regardless of how conveniently the longitude graduations lie parallel to the leg.

You measure a course of 90° and write it on the chart. What does the plot require you to write?

C 090, placed above the course line, with speed as S 8 below it Bowditch Ch. 8 §802. Course above, speed below, is the standard label .

A candidate reads a direction off an inner graduation of the rose and reports it as the true course. Why is the answer wrong?

The true course is read where the ruler crosses the outer (true) ring . A value taken from any other graduation on the rose is not a true direction, and the plot labelled with it misstates the course.

Your leg is 26 miles long and your dividers open to no more than 8 minutes on the latitude scale. How do you measure it?

Set the dividers to a round span on the latitude scale abreast of the leg — 5 minutes, or 5 nautical miles — and step along the line, counting the steps, then carry the remainder back to the same part of the scale and read it directly. One minute of latitude is one nautical mile , so five whole steps plus a 1.0-minute remainder gives 26.0 miles.

You are asked for the course from a lighted buoy to a charted rock on a Mercator chart, and the leg is 40 miles long. How many course values does the plot produce?

One. A rhumb line — a track of constant bearing — appears as a straight line on a Mercator chart Bowditch Ch. 4 §402, so the single straight line joining the two points carries one true course over its whole length.

Two of the four offered answers give the same course but distances differing by 1.8 miles. What does that tell you about where to spend your remaining time?

On the distance measurement, not the rose. Identical courses in two options means the course reading is not what separates them; the distinguishing operation is the divider span and the scale it was read against, which must be the latitude scale at the latitude of the line , .